CN-122021234-A - GNSS-R soil humidity inversion method based on Kalman filtering and physical information

CN122021234ACN 122021234 ACN122021234 ACN 122021234ACN-122021234-A

Abstract

The invention relates to the technical field of hydrological remote sensing, and discloses a GNSS-R soil humidity inversion method based on Kalman filtering and physical information, which constructs a composite state vector formed by physical information neural network parameters and soil physical parameters, and establishes a double-layer collaborative framework, wherein the internal circulation utilizes the physical information neural network to advance state evolution under the constraint of a physical equation to generate a priori set; and the outer loop adopts a set Kalman filter, and based on GNSS-R observation data, network weights and soil physical parameters in the composite state vector are synchronously updated by using cross covariance. The invention solves the precision bottleneck caused by the uncertainty of the physical model parameters, realizes the synchronous inversion of the soil humidity profile and the self-adaptive calibration of the model parameters by using the earth surface observation data, reduces the inversion error, ensures the physical consistency of the results and provides complete uncertainty quantification.

Inventors

HONG LEI
JIN SHUANGGEN
LIANG HUI

Assignees

河南理工大学

Dates

Publication Date: 20260512
Application Date: 20251204

Claims (10)

1. GNSS-R soil humidity inversion method based on Kalman filtering and physical information is characterized by comprising the following steps: S1, executing the steps of defining a composite state vector and initializing, namely defining the composite state vector formed by trainable network parameters of a physical information neural network and soil physical parameters together, and generating an initial state set comprising a plurality of members; s2, executing a forecasting step based on a physical information neural network set, namely independently running a corresponding physical information neural network for each member in the initial state set or the analysis state set at the previous moment, and forward pushing a composite state vector of each member on a time axis by minimizing a composite loss function containing physical constraint to generate a priori state set; S3, performing analysis updating based on ensemble Kalman filtering, namely acquiring real GNSS-R observation data at the current moment, mapping the prior state ensemble to an observation space by using a nonlinear observation operator to obtain a predicted observation value ensemble, constructing a Kalman gain matrix based on statistical characteristics of the prior state ensemble and the predicted observation value ensemble, and correcting each member in the prior state ensemble by using the Kalman gain matrix to generate an analysis state ensemble; And S4, executing product generation and loop iteration, namely executing set statistical operation based on the analysis state set to determine inversion results of soil humidity and soil physical parameters, and returning the analysis state set as an initial set of the next time step to execute the forecasting step to perform sequential assimilation treatment.
2. The GNSS-R soil moisture inversion method based on Kalman filtering and physical information of claim 1 wherein in said S1 step, the soil physical parameters in said composite state vector comprise physical constants describing soil hydraulic characteristics; The generating an initial state set comprising a plurality of members includes determining an initial center state vector and applying random perturbations to the initial center state vector to generate an initial state set comprising a set number of members, wherein each member comprises a set of independent physical information neural network parameters and a set of independent soil physical parameters.
3. The GNSS-R soil moisture inversion method based on kalman filtering and physical information according to claim 1, wherein in the step S2, the composite loss function is composed of a weighted sum of a physical loss term, a boundary condition loss term, and an initial condition loss term; The step of minimizing the composite loss function containing physical constraints comprises the step of iteratively updating trainable network parameters of the physical information neural network of each member by adopting a gradient-based optimization algorithm until the composite loss function converges or reaches a preset training round number, thereby completing the time propulsion of the state.
4. The GNSS-R soil moisture inversion method based on kalman filtering and physical information according to claim 3, wherein the physical loss term is used to restrict the output of the physical information neural network to satisfy the richardson-richarz equation; in calculating the physical loss term, the soil specific water capacity and the unsaturated water conductivity in the richardson-richarz equation are not fixed constants, but are functions determined by the soil physical parameters in the composite state vector of the current member, so that the soil physical parameters to be inverted are coupled into the physical constraints of the physical information neural network.
5. The GNSS-R soil moisture inversion method based on kalman filtering and physical information according to claim 4, wherein the calculation process of the physical loss term includes: randomly sampling configuration points in a space-time solving domain; Directly deriving a calculation diagram of the physical information neural network by utilizing an automatic differentiation technology, and obtaining partial derivatives of output variables relative to time and space coordinates; Substituting the partial derivative into a Lechasen-Lechaz equation, and calculating the difference value of the left and right ends of the equation on each configuration point as a physical equation residual.
6. The GNSS-R soil moisture inversion method based on kalman filtering and physical information according to claim 1, wherein in the step S3, the nonlinear observer is used to map the soil moisture physical state space output by the physical information neural network to the GNSS-R reflectivity observation space; The set of predicted observations is derived from a priori state vectors respectively applied by the nonlinear observation operator to each member of the set of a priori states.
7. The GNSS-R soil moisture inversion method based on kalman filtering and physical information according to claim 1, wherein in the step S3, the constructing a kalman gain matrix based on the statistical characteristics of the prior state set and the predicted observation value set specifically includes: Calculating a cross covariance matrix between the prior state and the predicted observation value by utilizing the deviation of each member of the prior state set relative to the set mean value and the deviation of each member of the predicted observation value set relative to the set mean value; calculating the sum of an auto-covariance matrix and an observation error covariance matrix of the predicted observation value set, and performing matrix inversion operation on the summation result; Multiplying the cross covariance matrix with the matrix inversion operation result to obtain a Kalman gain matrix; wherein the cross covariance matrix quantifies a statistical correlation between the variation of each component in the composite state vector and the observed value variation.
8. The GNSS-R soil moisture inversion method based on kalman filtering and physical information according to claim 7, wherein said correcting each member of said a priori state set comprises: calculating the difference value of the real GNSS-R observation data and the corresponding member in the predicted observation value set to obtain an innovation vector, and superposing the innovation vector and the generated random observation disturbance vector; and mapping the information vector after the superposition disturbance back to a state space by using the Kalman gain matrix, and adding the information vector to the corresponding prior state vector, thereby realizing the following double updating: adjusting the weight and bias of the physical information neural network according to the observation error; And synchronously adjusting the physical parameters of the soil according to the observation errors.
9. The GNSS-R soil moisture inversion method based on kalman filtering and physical information according to claim 1, wherein in the step S1, the soil physical parameters specifically include a soil saturation water conductivity and a shape parameter in a van Genuchten-Mualem model; In the step S3, the correction of the soil physical parameter is indirectly implemented based on the covariance relation established by the soil physical parameter in the step S2 by influencing the soil humidity evolution through a control equation.
10. The GNSS-R soil moisture inversion method based on kalman filtering and physical information according to claim 1, wherein in the step S4, the determining the inversion result of the soil moisture and the soil physical parameters includes: carrying out average operation on all members in the analysis state set to obtain a mean value vector which is used as the best estimated value of the soil humidity vertical section, the soil physical parameters and the physical information neural network parameters at the current moment; And calculating the discrete degree of the analysis state set relative to the mean vector to obtain a covariance matrix, and extracting diagonal elements to determine a confidence interval and an uncertainty range of an inversion result.

Description

GNSS-R soil humidity inversion method based on Kalman filtering and physical information Technical Field The invention relates to the technical field of hydrological remote sensing, in particular to a GNSS-R soil humidity inversion method based on Kalman filtering and physical information. Background At present, accurate acquisition of soil humidity distribution is of great importance to modern agriculture management and hydrologic climate research. Because the earth surface soil moisture has stronger heterogeneity on the space-time scale, the conventional ground sparse site observation is difficult to meet the regional monitoring requirement. Remote sensing using global navigation satellite system reflection signals (GNSS-R) has become an important means for obtaining high resolution surface information. The technology utilizes the power and waveform characteristics of the reflected signals to invert the change of the dielectric constant of the earth surface by receiving the navigation satellite signals reflected by the earth surface, so as to calculate the soil humidity condition of the area. For the GNSS-R soil humidity inversion, the existing mainstream application mostly adopts a data assimilation or statistical regression mode. The method comprises the steps of generating a background field by running a land process model through an ensemble Kalman filter (EnKF), and fusing GNSS-R observation data into a model state by using Kalman gain at an observation time. Another common path is to use a deep neural network, train through a large amount of historical data, establish a nonlinear mapping relationship between reflectivity signals and soil humidity, and directly extract the surface water features from satellite signals. Existing inversion and assimilation techniques remain limited. The traditional EnKF framework generally regards soil hydraulic parameters as fixed constants, and cannot adapt to differences of soil physical characteristics of different areas, and the model prediction has systematic deviation which is difficult to eliminate due to the stiffness of the parameters. The neural network driven by pure data has strong fitting capability, but lacks of physical mechanism constraint, the output result of the neural network often does not meet the water movement control equation, and physical spurious violating the law of conservation of mass is easy to occur. In addition, the existing method focuses on point estimation of state quantity, confidence interval of inversion results cannot be effectively quantized, and especially uncertainty estimation on deep soil physical parameters is insufficient in the current technical means. Therefore, the invention provides a GNSS-R soil humidity inversion method based on Kalman filtering and physical information, so as to solve the defects in the prior art. Disclosure of Invention Aiming at the defects of the prior art, the invention provides a GNSS-R soil humidity inversion method based on Kalman filtering and physical information, which solves the problems of limited inversion precision and difficult uncertainty quantification caused by difficult self-adaptive calibration of soil physical parameters and lack of physical consistency constraint of a pure data driving model in the existing GNSS-R soil humidity inversion method. In order to achieve the above purpose, the invention is realized by the following technical scheme: A GNSS-R soil humidity inversion method based on Kalman filtering and physical information comprises the following steps: Firstly, executing the steps of defining a composite state vector and initializing, defining the composite state vector formed by the trainable network parameters of a physical information neural network and the physical parameters of soil, and generating an initial state set comprising a plurality of members; Secondly, executing a forecasting step based on a physical information neural network set, independently running a corresponding physical information neural network for each member in an initial state set or an analysis state set at the previous moment, and advancing a composite state vector of each member on a time axis by minimizing a composite loss function containing physical constraint to generate a priori state set; Then, an analysis updating step based on ensemble Kalman filtering is carried out, real GNSS-R observation data at the current moment is obtained, a priori state ensemble is mapped to an observation space by using a nonlinear observation operator to obtain a predicted observation value ensemble, a Kalman gain matrix is calculated, and each member in the priori state ensemble is corrected by using the Kalman gain matrix to generate an analysis state ensemble; and finally, executing the steps of product generation and loop iteration, calculating statistical characteristics based on the analysis state set to determine inversion results of soil humidity and soil physical parameters, and returning t